Imaging of micro-steps on as-grown surface of sapphire with X-ray phase contrast technique

Abstract

Basal-faceted sapphire ribbons grown using the Stepanov–LaBelle technology have a low density of surface steps. We present our results on a study of steps on the surface of a ribbon, misoriented relative to the singular face (0001) by several arc minutes. The ribbon has been characterized by means of in-line phase contrast imaging technique at Pohang Light Source, South Korea. It was shown for the first time that a step height of about 1 μm can be determined directly from an image. The step height obtained using the phase contrast method was confirmed by atomic force microscopy measurements. We have found that the experimental contrast matches the theoretical simulations only if the calculated intensity profile has been convolved with a Gaussian function. The full width at half maximum of the Gaussian was independently got from previous measurements. We have obtained an analytical solution in the case of theoretical fully coherent phase contrast image. The inverse problem is easy to solve, since there is a direct proportionality between the contrast and the step height.